Strange stretching of mesh when using automatic weights
The automatic weights didnt paint the entire mesh the way you want it.

You can manually weight paint the mesh 
here is a youtube tutorial:
https://www.youtube.com/watch?v=S0VS0IVylzg

Or just try changing the "bone envelope" and parent the bones to the mesh with automatic bone envelopes

here is a tutorial:https://www.youtube.com/watch?v=wBLv6oa60_k

But either way you will probably want to tweak it to make it perfect by manually weight painting a little